John, List:
JFS: I am happy to say that I completely agree with Jon's note below.
However, the following passage from another note is misleading about
Peirce, Euclid, and mathematical practice from ancient times to the present.
The quoted passage is from my same note below.
JFS: In mathematical
Jerry, Jon, List,
JLRC: If the critical concept that is under scrutiny here the issue of “graphs
of graphs” , how is this related to the arithmetical notion of division?
I agree with Jon's explanation below that Peirce did not use the word
"division" to mean the numerical operation of dividing
Jerry, List:
In this context, "division" simply refers to Peirce's 1903 *organization *of
Existential Graphs (EGs) into distinct Alpha, Beta, and Gamma parts. Alpha
implements propositional logic, Beta implements a version of first-order
predicate logic by adding the line of identity, and Gamma im
Jerry, List:
No one is claiming that Peirce ever used the *term *"metalanguage," only
the *concept*. Specifically, he provided a Gamma EG notation for asserting
a proposition about a proposition--the lightly drawn (1898) or dotted
(1903) oval for treating a complete proposition as a *subject *that
